Anomaly matching in the symmetry broken phase: Domain walls, CPT, and the Smith isomorphism

Abstract

Symmetries in Quantum Field Theory may have 't Hooft anomalies. If the symmetry is unbroken in the vacuum, the anomaly implies a nontrivial low-energy limit, such as gapless modes or a topological field theory. If the symmetry is spontaneously broken, for the continuous case, the anomaly implies low-energy theorems about certain couplings of the Goldstone modes. Here we study the case of spontaneously broken discrete symmetries, such as Z2 and T . Symmetry breaking leads to domain walls, and the physics of the domain walls is constrained by the anomaly. We investigate how the physics of the domain walls leads to a matching of the original discrete anomaly. We analyze the symmetry structure on the domain wall, which requires a careful analysis of some properties of the unbreakable CP T symmetry. We demonstrate the general results on some examples and we explain in detail the mod 4 periodic structure that arises in the Z2 and T case. This gives a physical interpretation for the Smith isomorphism, which we also extend to more general abelian groups. We show that via symmetry breaking and the analysis of the physics on the wall, the computations of certain discrete anomalies are greatly simplified. Using these results we perform new consistency checks on the infrared phases of 2 + 1 dimensional QCD. * which by construction leaves the boundary conditions invariant and therefore indeed acts on the wall! But observe that this is an anti-unitary symmetry, since CP ⊥ T is anti-unitary. Thus, the correct answer to the question about the fate of the spontaneously broken, unitary, Z 2 symmetry is that it becomes some anti-unitary symmetry acting on the wall.By the same argument, if we began with a spontaneously broken anti-unitary Z 2 symmetry, the domain wall would inherit a unitary Z 2 symmetry. In fact, we will derive a 4-periodic dimensional

Gauge enhanced quantum criticality and time reversal deconfined domain wall: SU(2) Yang-Mills dynamics with topological terms

“…The reversed sign of the Chern Simons level reflects the reversal of the direction of the anomaly inflow under T . A useful observation [34,35] is that T can be modified to be the symmetry of SU(2) 1 by multiplying an unbreakable CP ⊥ T in 4d. (Analogue phenomenon and more general relation to the Smith Isomorphism have been discussed by Hason, Komargodski and Thorngren [34] and independently by Cordova, Ohmori, Shao and Yan [35].…”

“…A useful observation [34,35] is that T can be modified to be the symmetry of SU(2) 1 by multiplying an unbreakable CP ⊥ T in 4d. (Analogue phenomenon and more general relation to the Smith Isomorphism have been discussed by Hason, Komargodski and Thorngren [34] and independently by Cordova, Ohmori, Shao and Yan [35]. See also the talk [36] by Thorngren. We apply this general idea to the special context: the domain wall of SU(2) Yang-Mills.)…”

Musings on the current status of HEP

“…Sorry for the pun... After [12,13,14] a large number of non-trivial applications has been worked out. Many relevant references can be found in [18,19].…”

Deconfinement on axion domain walls

“…We refer to these constraints as "generalized 't Hooft anomalies." Their study is evolving too rapidly to allow us to do justice to all interesting aspects currently investigated; we only note that complementary aspects of theories closely related to the ones we consider here are the subject of [6][7][8][9][10][11][12][13][14][15][16][17][18].…”